4024/12 May/Jun 2025, Question 16: Finding the Median and Quartiles
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
Using a cumulative frequency graph for 80 people's journey times, estimate median and interquartile range, count people taking 40 minutes or more, then judge Jay's consistency claim comparing two IQRs.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (ai) · 1 mark
Read the median journey time from the cumulative frequency curve.
- 1Median at cumulative frequency 80 ÷ 2 = 40
- 2Read across to the curve and down: 32 minutes
Answer32
Part (aii) · 2 marks
Find the interquartile range from the cumulative frequency curve.
- 1Lower quartile at 20: 25 minutes; upper quartile at 60: 35 minutes
- 2IQR = 35 − 25 = 10 minutes
Answer10
Part (aiii) · 2 marks
Use the curve to estimate how many people had journey times of 40 minutes or more.
- 1Read up from 40 minutes: cumulative frequency = 72
- 280 − 72 = 8 people
Answer8
Part (b) · 1 mark
Compare the two interquartile ranges to decide whether Jay's statement about consistency is correct, explaining why.
- 1Home to work IQR = 10 minutes, work to home IQR = 15 minutes
- 2Yes: the IQR is lower for home to work, so those times are more consistent
AnswerYes, IQR is lower [for journey time from home to work]
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